Properties

Label 117.4.g.e.55.3
Level $117$
Weight $4$
Character 117.55
Analytic conductor $6.903$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(55,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 29x^{6} + 2x^{5} + 595x^{4} - 288x^{3} + 2526x^{2} + 1872x + 6084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.3
Root \(1.18088 + 2.04535i\) of defining polynomial
Character \(\chi\) \(=\) 117.55
Dual form 117.4.g.e.100.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.18088 + 2.04535i) q^{2} +(1.21104 - 2.09758i) q^{4} -6.42208 q^{5} +(14.7469 - 25.5424i) q^{7} +24.6145 q^{8} +O(q^{10})\) \(q+(1.18088 + 2.04535i) q^{2} +(1.21104 - 2.09758i) q^{4} -6.42208 q^{5} +(14.7469 - 25.5424i) q^{7} +24.6145 q^{8} +(-7.58371 - 13.1354i) q^{10} +(-0.312358 - 0.541019i) q^{11} +(44.3948 + 15.0368i) q^{13} +69.6575 q^{14} +(19.3785 + 33.5645i) q^{16} +(43.8645 - 75.9756i) q^{17} +(-41.4009 + 71.7085i) q^{19} +(-7.77738 + 13.4708i) q^{20} +(0.737715 - 1.27776i) q^{22} +(-37.3989 - 64.7767i) q^{23} -83.7569 q^{25} +(21.6695 + 108.559i) q^{26} +(-35.7182 - 61.8657i) q^{28} +(113.165 + 196.007i) q^{29} +173.660 q^{31} +(52.6906 - 91.2627i) q^{32} +207.195 q^{34} +(-94.7059 + 164.035i) q^{35} +(-56.0102 - 97.0124i) q^{37} -195.558 q^{38} -158.076 q^{40} +(-133.506 - 231.238i) q^{41} +(-191.725 + 332.077i) q^{43} -1.51311 q^{44} +(88.3272 - 152.987i) q^{46} -337.380 q^{47} +(-263.443 - 456.297i) q^{49} +(-98.9070 - 171.312i) q^{50} +(85.3046 - 74.9115i) q^{52} +146.354 q^{53} +(2.00598 + 3.47447i) q^{55} +(362.988 - 628.713i) q^{56} +(-267.268 + 462.922i) q^{58} +(-264.587 + 458.277i) q^{59} +(-101.636 + 176.038i) q^{61} +(205.072 + 355.195i) q^{62} +558.941 q^{64} +(-285.107 - 96.5673i) q^{65} +(-60.7484 - 105.219i) q^{67} +(-106.243 - 184.019i) q^{68} -447.346 q^{70} +(-330.657 + 572.715i) q^{71} +167.341 q^{73} +(132.283 - 229.120i) q^{74} +(100.276 + 173.684i) q^{76} -18.4253 q^{77} -101.399 q^{79} +(-124.450 - 215.554i) q^{80} +(315.308 - 546.130i) q^{82} +506.985 q^{83} +(-281.702 + 487.921i) q^{85} -905.617 q^{86} +(-7.68852 - 13.3169i) q^{88} +(701.166 + 1214.45i) q^{89} +(1038.76 - 912.204i) q^{91} -181.166 q^{92} +(-398.405 - 690.058i) q^{94} +(265.880 - 460.518i) q^{95} +(-951.445 + 1647.95i) q^{97} +(622.191 - 1077.67i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 22 q^{4} + 12 q^{5} + 14 q^{7} - 108 q^{8} + 62 q^{10} + 40 q^{11} - 60 q^{13} - 80 q^{14} - 122 q^{16} + 98 q^{17} - 124 q^{19} - 466 q^{20} - 220 q^{22} + 104 q^{23} - 116 q^{25} - 14 q^{26} + 144 q^{28} + 194 q^{29} + 52 q^{31} + 654 q^{32} + 2124 q^{34} + 88 q^{35} - 102 q^{37} - 664 q^{38} - 1996 q^{40} - 1054 q^{41} - 450 q^{43} + 88 q^{44} + 172 q^{46} + 192 q^{47} - 1070 q^{49} + 996 q^{50} + 2280 q^{52} - 524 q^{53} - 204 q^{55} + 2164 q^{56} - 722 q^{58} + 308 q^{59} + 928 q^{61} + 2780 q^{62} + 2052 q^{64} - 2346 q^{65} + 1134 q^{67} + 1786 q^{68} - 4648 q^{70} + 1064 q^{71} + 1904 q^{73} + 1158 q^{74} + 1708 q^{76} - 5016 q^{77} - 1492 q^{79} - 2922 q^{80} - 1734 q^{82} + 808 q^{83} + 1394 q^{85} - 6336 q^{86} - 3060 q^{88} + 1620 q^{89} + 3278 q^{91} - 664 q^{92} + 772 q^{94} + 2204 q^{95} - 2166 q^{97} - 1906 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18088 + 2.04535i 0.417505 + 0.723139i 0.995688 0.0927678i \(-0.0295714\pi\)
−0.578183 + 0.815907i \(0.696238\pi\)
\(3\) 0 0
\(4\) 1.21104 2.09758i 0.151380 0.262198i
\(5\) −6.42208 −0.574408 −0.287204 0.957869i \(-0.592726\pi\)
−0.287204 + 0.957869i \(0.592726\pi\)
\(6\) 0 0
\(7\) 14.7469 25.5424i 0.796259 1.37916i −0.125778 0.992058i \(-0.540143\pi\)
0.922037 0.387102i \(-0.126524\pi\)
\(8\) 24.6145 1.08782
\(9\) 0 0
\(10\) −7.58371 13.1354i −0.239818 0.415377i
\(11\) −0.312358 0.541019i −0.00856176 0.0148294i 0.861713 0.507396i \(-0.169392\pi\)
−0.870275 + 0.492567i \(0.836059\pi\)
\(12\) 0 0
\(13\) 44.3948 + 15.0368i 0.947146 + 0.320804i
\(14\) 69.6575 1.32977
\(15\) 0 0
\(16\) 19.3785 + 33.5645i 0.302788 + 0.524445i
\(17\) 43.8645 75.9756i 0.625807 1.08393i −0.362577 0.931954i \(-0.618103\pi\)
0.988384 0.151976i \(-0.0485635\pi\)
\(18\) 0 0
\(19\) −41.4009 + 71.7085i −0.499896 + 0.865845i −1.00000 0.000120110i \(-0.999962\pi\)
0.500104 + 0.865965i \(0.333295\pi\)
\(20\) −7.77738 + 13.4708i −0.0869538 + 0.150608i
\(21\) 0 0
\(22\) 0.737715 1.27776i 0.00714915 0.0123827i
\(23\) −37.3989 64.7767i −0.339052 0.587256i 0.645203 0.764012i \(-0.276773\pi\)
−0.984255 + 0.176756i \(0.943440\pi\)
\(24\) 0 0
\(25\) −83.7569 −0.670055
\(26\) 21.6695 + 108.559i 0.163452 + 0.818855i
\(27\) 0 0
\(28\) −35.7182 61.8657i −0.241075 0.417554i
\(29\) 113.165 + 196.007i 0.724625 + 1.25509i 0.959128 + 0.282973i \(0.0913205\pi\)
−0.234503 + 0.972115i \(0.575346\pi\)
\(30\) 0 0
\(31\) 173.660 1.00614 0.503070 0.864246i \(-0.332204\pi\)
0.503070 + 0.864246i \(0.332204\pi\)
\(32\) 52.6906 91.2627i 0.291077 0.504160i
\(33\) 0 0
\(34\) 207.195 1.04511
\(35\) −94.7059 + 164.035i −0.457378 + 0.792201i
\(36\) 0 0
\(37\) −56.0102 97.0124i −0.248865 0.431047i 0.714346 0.699793i \(-0.246724\pi\)
−0.963211 + 0.268745i \(0.913391\pi\)
\(38\) −195.558 −0.834835
\(39\) 0 0
\(40\) −158.076 −0.624850
\(41\) −133.506 231.238i −0.508538 0.880814i −0.999951 0.00988706i \(-0.996853\pi\)
0.491413 0.870927i \(-0.336481\pi\)
\(42\) 0 0
\(43\) −191.725 + 332.077i −0.679948 + 1.17770i 0.295048 + 0.955483i \(0.404664\pi\)
−0.974996 + 0.222222i \(0.928669\pi\)
\(44\) −1.51311 −0.00518431
\(45\) 0 0
\(46\) 88.3272 152.987i 0.283112 0.490364i
\(47\) −337.380 −1.04706 −0.523530 0.852007i \(-0.675385\pi\)
−0.523530 + 0.852007i \(0.675385\pi\)
\(48\) 0 0
\(49\) −263.443 456.297i −0.768057 1.33031i
\(50\) −98.9070 171.312i −0.279751 0.484543i
\(51\) 0 0
\(52\) 85.3046 74.9115i 0.227493 0.199776i
\(53\) 146.354 0.379308 0.189654 0.981851i \(-0.439263\pi\)
0.189654 + 0.981851i \(0.439263\pi\)
\(54\) 0 0
\(55\) 2.00598 + 3.47447i 0.00491794 + 0.00851813i
\(56\) 362.988 628.713i 0.866183 1.50027i
\(57\) 0 0
\(58\) −267.268 + 462.922i −0.605069 + 1.04801i
\(59\) −264.587 + 458.277i −0.583834 + 1.01123i 0.411185 + 0.911552i \(0.365115\pi\)
−0.995020 + 0.0996790i \(0.968218\pi\)
\(60\) 0 0
\(61\) −101.636 + 176.038i −0.213330 + 0.369499i −0.952755 0.303741i \(-0.901764\pi\)
0.739425 + 0.673239i \(0.235098\pi\)
\(62\) 205.072 + 355.195i 0.420068 + 0.727579i
\(63\) 0 0
\(64\) 558.941 1.09168
\(65\) −285.107 96.5673i −0.544048 0.184272i
\(66\) 0 0
\(67\) −60.7484 105.219i −0.110770 0.191859i 0.805311 0.592853i \(-0.201998\pi\)
−0.916081 + 0.400993i \(0.868665\pi\)
\(68\) −106.243 184.019i −0.189469 0.328170i
\(69\) 0 0
\(70\) −447.346 −0.763829
\(71\) −330.657 + 572.715i −0.552701 + 0.957306i 0.445378 + 0.895343i \(0.353069\pi\)
−0.998078 + 0.0619630i \(0.980264\pi\)
\(72\) 0 0
\(73\) 167.341 0.268299 0.134150 0.990961i \(-0.457170\pi\)
0.134150 + 0.990961i \(0.457170\pi\)
\(74\) 132.283 229.120i 0.207805 0.359928i
\(75\) 0 0
\(76\) 100.276 + 173.684i 0.151348 + 0.262143i
\(77\) −18.4253 −0.0272695
\(78\) 0 0
\(79\) −101.399 −0.144408 −0.0722042 0.997390i \(-0.523003\pi\)
−0.0722042 + 0.997390i \(0.523003\pi\)
\(80\) −124.450 215.554i −0.173924 0.301245i
\(81\) 0 0
\(82\) 315.308 546.130i 0.424634 0.735487i
\(83\) 506.985 0.670468 0.335234 0.942135i \(-0.391185\pi\)
0.335234 + 0.942135i \(0.391185\pi\)
\(84\) 0 0
\(85\) −281.702 + 487.921i −0.359468 + 0.622618i
\(86\) −905.617 −1.13553
\(87\) 0 0
\(88\) −7.68852 13.3169i −0.00931362 0.0161317i
\(89\) 701.166 + 1214.45i 0.835095 + 1.44643i 0.893953 + 0.448160i \(0.147921\pi\)
−0.0588586 + 0.998266i \(0.518746\pi\)
\(90\) 0 0
\(91\) 1038.76 912.204i 1.19661 1.05082i
\(92\) −181.166 −0.205303
\(93\) 0 0
\(94\) −398.405 690.058i −0.437153 0.757171i
\(95\) 265.880 460.518i 0.287144 0.497348i
\(96\) 0 0
\(97\) −951.445 + 1647.95i −0.995924 + 1.72499i −0.419849 + 0.907594i \(0.637917\pi\)
−0.576075 + 0.817397i \(0.695416\pi\)
\(98\) 622.191 1077.67i 0.641334 1.11082i
\(99\) 0 0
\(100\) −101.433 + 175.687i −0.101433 + 0.175687i
\(101\) 916.546 + 1587.50i 0.902968 + 1.56399i 0.823622 + 0.567139i \(0.191950\pi\)
0.0793462 + 0.996847i \(0.474717\pi\)
\(102\) 0 0
\(103\) 1446.99 1.38423 0.692115 0.721787i \(-0.256679\pi\)
0.692115 + 0.721787i \(0.256679\pi\)
\(104\) 1092.75 + 370.122i 1.03032 + 0.348976i
\(105\) 0 0
\(106\) 172.827 + 299.345i 0.158363 + 0.274292i
\(107\) −184.643 319.811i −0.166823 0.288947i 0.770478 0.637467i \(-0.220018\pi\)
−0.937301 + 0.348520i \(0.886684\pi\)
\(108\) 0 0
\(109\) −815.694 −0.716782 −0.358391 0.933572i \(-0.616675\pi\)
−0.358391 + 0.933572i \(0.616675\pi\)
\(110\) −4.73766 + 8.20587i −0.00410653 + 0.00711272i
\(111\) 0 0
\(112\) 1143.09 0.964392
\(113\) 895.282 1550.67i 0.745319 1.29093i −0.204726 0.978819i \(-0.565630\pi\)
0.950045 0.312112i \(-0.101036\pi\)
\(114\) 0 0
\(115\) 240.178 + 416.001i 0.194754 + 0.337324i
\(116\) 548.187 0.438775
\(117\) 0 0
\(118\) −1249.78 −0.975014
\(119\) −1293.73 2240.81i −0.996608 1.72618i
\(120\) 0 0
\(121\) 665.305 1152.34i 0.499853 0.865771i
\(122\) −480.079 −0.356265
\(123\) 0 0
\(124\) 210.309 364.266i 0.152309 0.263807i
\(125\) 1340.65 0.959293
\(126\) 0 0
\(127\) 22.6450 + 39.2223i 0.0158222 + 0.0274048i 0.873828 0.486235i \(-0.161630\pi\)
−0.858006 + 0.513640i \(0.828297\pi\)
\(128\) 238.518 + 413.125i 0.164705 + 0.285277i
\(129\) 0 0
\(130\) −139.163 697.176i −0.0938880 0.470357i
\(131\) −1051.82 −0.701511 −0.350756 0.936467i \(-0.614075\pi\)
−0.350756 + 0.936467i \(0.614075\pi\)
\(132\) 0 0
\(133\) 1221.07 + 2114.96i 0.796093 + 1.37887i
\(134\) 143.473 248.503i 0.0924940 0.160204i
\(135\) 0 0
\(136\) 1079.70 1870.10i 0.680763 1.17912i
\(137\) −771.471 + 1336.23i −0.481104 + 0.833296i −0.999765 0.0216836i \(-0.993097\pi\)
0.518661 + 0.854980i \(0.326431\pi\)
\(138\) 0 0
\(139\) −18.9322 + 32.7915i −0.0115526 + 0.0200097i −0.871744 0.489962i \(-0.837011\pi\)
0.860191 + 0.509971i \(0.170344\pi\)
\(140\) 229.385 + 397.306i 0.138475 + 0.239847i
\(141\) 0 0
\(142\) −1561.87 −0.923020
\(143\) −5.73186 28.7153i −0.00335190 0.0167923i
\(144\) 0 0
\(145\) −726.752 1258.77i −0.416231 0.720933i
\(146\) 197.610 + 342.271i 0.112016 + 0.194018i
\(147\) 0 0
\(148\) −271.322 −0.150693
\(149\) −911.199 + 1578.24i −0.500995 + 0.867749i 0.499004 + 0.866600i \(0.333699\pi\)
−0.999999 + 0.00114972i \(0.999634\pi\)
\(150\) 0 0
\(151\) −3239.36 −1.74580 −0.872900 0.487899i \(-0.837763\pi\)
−0.872900 + 0.487899i \(0.837763\pi\)
\(152\) −1019.06 + 1765.07i −0.543795 + 0.941881i
\(153\) 0 0
\(154\) −21.7580 37.6860i −0.0113851 0.0197197i
\(155\) −1115.26 −0.577934
\(156\) 0 0
\(157\) 830.565 0.422206 0.211103 0.977464i \(-0.432295\pi\)
0.211103 + 0.977464i \(0.432295\pi\)
\(158\) −119.740 207.396i −0.0602912 0.104427i
\(159\) 0 0
\(160\) −338.383 + 586.096i −0.167197 + 0.289594i
\(161\) −2206.07 −1.07989
\(162\) 0 0
\(163\) 1039.95 1801.25i 0.499725 0.865550i −0.500275 0.865867i \(-0.666768\pi\)
1.00000 0.000317114i \(0.000100941\pi\)
\(164\) −646.721 −0.307930
\(165\) 0 0
\(166\) 598.689 + 1036.96i 0.279923 + 0.484842i
\(167\) 42.9895 + 74.4600i 0.0199199 + 0.0345023i 0.875814 0.482650i \(-0.160326\pi\)
−0.855894 + 0.517152i \(0.826992\pi\)
\(168\) 0 0
\(169\) 1744.79 + 1335.11i 0.794170 + 0.607696i
\(170\) −1330.62 −0.600319
\(171\) 0 0
\(172\) 464.373 + 804.317i 0.205861 + 0.356562i
\(173\) 1353.23 2343.87i 0.594708 1.03006i −0.398880 0.917003i \(-0.630601\pi\)
0.993588 0.113061i \(-0.0360655\pi\)
\(174\) 0 0
\(175\) −1235.16 + 2139.35i −0.533538 + 0.924114i
\(176\) 12.1060 20.9682i 0.00518480 0.00898035i
\(177\) 0 0
\(178\) −1655.99 + 2868.25i −0.697312 + 1.20778i
\(179\) −2201.05 3812.33i −0.919074 1.59188i −0.800825 0.598899i \(-0.795605\pi\)
−0.118250 0.992984i \(-0.537728\pi\)
\(180\) 0 0
\(181\) −1673.98 −0.687435 −0.343718 0.939073i \(-0.611686\pi\)
−0.343718 + 0.939073i \(0.611686\pi\)
\(182\) 3092.43 + 1047.42i 1.25948 + 0.426594i
\(183\) 0 0
\(184\) −920.553 1594.44i −0.368826 0.638826i
\(185\) 359.702 + 623.021i 0.142950 + 0.247597i
\(186\) 0 0
\(187\) −54.8057 −0.0214320
\(188\) −408.580 + 707.681i −0.158504 + 0.274537i
\(189\) 0 0
\(190\) 1255.89 0.479536
\(191\) −145.059 + 251.249i −0.0549533 + 0.0951819i −0.892193 0.451654i \(-0.850834\pi\)
0.837240 + 0.546835i \(0.184168\pi\)
\(192\) 0 0
\(193\) −519.750 900.233i −0.193847 0.335752i 0.752675 0.658392i \(-0.228763\pi\)
−0.946522 + 0.322640i \(0.895430\pi\)
\(194\) −4494.18 −1.66321
\(195\) 0 0
\(196\) −1276.16 −0.465073
\(197\) 709.352 + 1228.63i 0.256544 + 0.444348i 0.965314 0.261092i \(-0.0840827\pi\)
−0.708769 + 0.705440i \(0.750749\pi\)
\(198\) 0 0
\(199\) 1194.19 2068.40i 0.425398 0.736810i −0.571060 0.820908i \(-0.693468\pi\)
0.996457 + 0.0840980i \(0.0268009\pi\)
\(200\) −2061.63 −0.728897
\(201\) 0 0
\(202\) −2164.66 + 3749.31i −0.753987 + 1.30594i
\(203\) 6675.32 2.30796
\(204\) 0 0
\(205\) 857.383 + 1485.03i 0.292108 + 0.505946i
\(206\) 1708.72 + 2959.59i 0.577922 + 1.00099i
\(207\) 0 0
\(208\) 355.601 + 1781.48i 0.118541 + 0.593861i
\(209\) 51.7276 0.0171200
\(210\) 0 0
\(211\) −2170.72 3759.81i −0.708241 1.22671i −0.965509 0.260369i \(-0.916156\pi\)
0.257268 0.966340i \(-0.417178\pi\)
\(212\) 177.241 306.990i 0.0574195 0.0994536i
\(213\) 0 0
\(214\) 436.083 755.317i 0.139299 0.241273i
\(215\) 1231.27 2132.63i 0.390568 0.676483i
\(216\) 0 0
\(217\) 2560.95 4435.70i 0.801147 1.38763i
\(218\) −963.237 1668.38i −0.299260 0.518333i
\(219\) 0 0
\(220\) 9.71730 0.00297791
\(221\) 3089.78 2713.34i 0.940459 0.825878i
\(222\) 0 0
\(223\) −2307.69 3997.03i −0.692978 1.20027i −0.970858 0.239657i \(-0.922965\pi\)
0.277880 0.960616i \(-0.410368\pi\)
\(224\) −1554.05 2691.69i −0.463545 0.802884i
\(225\) 0 0
\(226\) 4228.89 1.24470
\(227\) −1081.72 + 1873.59i −0.316283 + 0.547817i −0.979709 0.200424i \(-0.935768\pi\)
0.663427 + 0.748241i \(0.269101\pi\)
\(228\) 0 0
\(229\) 1859.48 0.536584 0.268292 0.963338i \(-0.413541\pi\)
0.268292 + 0.963338i \(0.413541\pi\)
\(230\) −567.244 + 982.496i −0.162622 + 0.281669i
\(231\) 0 0
\(232\) 2785.49 + 4824.60i 0.788259 + 1.36531i
\(233\) −2866.87 −0.806073 −0.403037 0.915184i \(-0.632045\pi\)
−0.403037 + 0.915184i \(0.632045\pi\)
\(234\) 0 0
\(235\) 2166.68 0.601440
\(236\) 640.849 + 1109.98i 0.176762 + 0.306160i
\(237\) 0 0
\(238\) 3055.49 5292.27i 0.832177 1.44137i
\(239\) −1893.55 −0.512485 −0.256242 0.966613i \(-0.582484\pi\)
−0.256242 + 0.966613i \(0.582484\pi\)
\(240\) 0 0
\(241\) 906.788 1570.60i 0.242371 0.419798i −0.719018 0.694991i \(-0.755408\pi\)
0.961389 + 0.275193i \(0.0887416\pi\)
\(242\) 3142.58 0.834764
\(243\) 0 0
\(244\) 246.170 + 426.379i 0.0645878 + 0.111869i
\(245\) 1691.85 + 2930.38i 0.441178 + 0.764142i
\(246\) 0 0
\(247\) −2916.25 + 2560.95i −0.751241 + 0.659713i
\(248\) 4274.56 1.09449
\(249\) 0 0
\(250\) 1583.15 + 2742.10i 0.400509 + 0.693703i
\(251\) 2081.16 3604.67i 0.523353 0.906474i −0.476278 0.879295i \(-0.658014\pi\)
0.999631 0.0271788i \(-0.00865235\pi\)
\(252\) 0 0
\(253\) −23.3636 + 40.4670i −0.00580577 + 0.0100559i
\(254\) −53.4821 + 92.6337i −0.0132117 + 0.0228833i
\(255\) 0 0
\(256\) 1672.44 2896.75i 0.408310 0.707214i
\(257\) 2992.65 + 5183.42i 0.726368 + 1.25811i 0.958409 + 0.285400i \(0.0921263\pi\)
−0.232041 + 0.972706i \(0.574540\pi\)
\(258\) 0 0
\(259\) −3303.91 −0.792645
\(260\) −547.833 + 481.087i −0.130674 + 0.114753i
\(261\) 0 0
\(262\) −1242.07 2151.34i −0.292884 0.507290i
\(263\) 287.309 + 497.634i 0.0673621 + 0.116675i 0.897739 0.440527i \(-0.145208\pi\)
−0.830377 + 0.557202i \(0.811875\pi\)
\(264\) 0 0
\(265\) −939.899 −0.217877
\(266\) −2883.88 + 4995.03i −0.664745 + 1.15137i
\(267\) 0 0
\(268\) −294.275 −0.0670734
\(269\) 3174.30 5498.06i 0.719482 1.24618i −0.241723 0.970345i \(-0.577712\pi\)
0.961205 0.275835i \(-0.0889542\pi\)
\(270\) 0 0
\(271\) 1639.19 + 2839.16i 0.367431 + 0.636408i 0.989163 0.146821i \(-0.0469042\pi\)
−0.621732 + 0.783230i \(0.713571\pi\)
\(272\) 3400.11 0.757948
\(273\) 0 0
\(274\) −3644.06 −0.803452
\(275\) 26.1621 + 45.3141i 0.00573685 + 0.00993652i
\(276\) 0 0
\(277\) −1976.09 + 3422.68i −0.428633 + 0.742415i −0.996752 0.0805318i \(-0.974338\pi\)
0.568119 + 0.822947i \(0.307671\pi\)
\(278\) −89.4267 −0.0192930
\(279\) 0 0
\(280\) −2331.14 + 4037.64i −0.497543 + 0.861769i
\(281\) 411.389 0.0873360 0.0436680 0.999046i \(-0.486096\pi\)
0.0436680 + 0.999046i \(0.486096\pi\)
\(282\) 0 0
\(283\) 2936.39 + 5085.98i 0.616785 + 1.06830i 0.990068 + 0.140586i \(0.0448987\pi\)
−0.373283 + 0.927717i \(0.621768\pi\)
\(284\) 800.877 + 1387.16i 0.167335 + 0.289834i
\(285\) 0 0
\(286\) 51.9640 45.6330i 0.0107437 0.00943474i
\(287\) −7875.18 −1.61971
\(288\) 0 0
\(289\) −1391.70 2410.49i −0.283268 0.490635i
\(290\) 1716.42 2972.92i 0.347556 0.601985i
\(291\) 0 0
\(292\) 202.657 351.012i 0.0406151 0.0703474i
\(293\) −250.478 + 433.841i −0.0499423 + 0.0865026i −0.889916 0.456125i \(-0.849237\pi\)
0.839974 + 0.542627i \(0.182570\pi\)
\(294\) 0 0
\(295\) 1699.20 2943.09i 0.335359 0.580859i
\(296\) −1378.66 2387.91i −0.270720 0.468900i
\(297\) 0 0
\(298\) −4304.07 −0.836671
\(299\) −686.281 3438.11i −0.132738 0.664986i
\(300\) 0 0
\(301\) 5654.70 + 9794.24i 1.08283 + 1.87552i
\(302\) −3825.31 6625.62i −0.728879 1.26246i
\(303\) 0 0
\(304\) −3209.14 −0.605451
\(305\) 652.713 1130.53i 0.122539 0.212243i
\(306\) 0 0
\(307\) −5975.57 −1.11089 −0.555446 0.831553i \(-0.687452\pi\)
−0.555446 + 0.831553i \(0.687452\pi\)
\(308\) −22.3137 + 38.6485i −0.00412805 + 0.00715000i
\(309\) 0 0
\(310\) −1316.99 2281.09i −0.241290 0.417927i
\(311\) −44.4925 −0.00811234 −0.00405617 0.999992i \(-0.501291\pi\)
−0.00405617 + 0.999992i \(0.501291\pi\)
\(312\) 0 0
\(313\) 9957.78 1.79823 0.899117 0.437709i \(-0.144210\pi\)
0.899117 + 0.437709i \(0.144210\pi\)
\(314\) 980.798 + 1698.79i 0.176273 + 0.305313i
\(315\) 0 0
\(316\) −122.798 + 212.692i −0.0218605 + 0.0378636i
\(317\) −7752.29 −1.37354 −0.686770 0.726875i \(-0.740972\pi\)
−0.686770 + 0.726875i \(0.740972\pi\)
\(318\) 0 0
\(319\) 70.6956 122.448i 0.0124081 0.0214915i
\(320\) −3589.56 −0.627070
\(321\) 0 0
\(322\) −2605.11 4512.18i −0.450860 0.780913i
\(323\) 3632.07 + 6290.92i 0.625677 + 1.08370i
\(324\) 0 0
\(325\) −3718.37 1259.43i −0.634640 0.214956i
\(326\) 4912.23 0.834550
\(327\) 0 0
\(328\) −3286.17 5691.81i −0.553196 0.958163i
\(329\) −4975.31 + 8617.49i −0.833732 + 1.44407i
\(330\) 0 0
\(331\) 669.427 1159.48i 0.111163 0.192540i −0.805076 0.593171i \(-0.797876\pi\)
0.916240 + 0.400631i \(0.131209\pi\)
\(332\) 613.979 1063.44i 0.101495 0.175795i
\(333\) 0 0
\(334\) −101.531 + 175.857i −0.0166333 + 0.0288097i
\(335\) 390.131 + 675.726i 0.0636272 + 0.110206i
\(336\) 0 0
\(337\) 3788.95 0.612454 0.306227 0.951958i \(-0.400933\pi\)
0.306227 + 0.951958i \(0.400933\pi\)
\(338\) −670.368 + 5145.31i −0.107879 + 0.828011i
\(339\) 0 0
\(340\) 682.303 + 1181.78i 0.108833 + 0.188504i
\(341\) −54.2441 93.9536i −0.00861432 0.0149204i
\(342\) 0 0
\(343\) −5423.53 −0.853770
\(344\) −4719.21 + 8173.91i −0.739659 + 1.28113i
\(345\) 0 0
\(346\) 6392.03 0.993173
\(347\) 3897.58 6750.80i 0.602977 1.04439i −0.389391 0.921072i \(-0.627315\pi\)
0.992368 0.123314i \(-0.0393521\pi\)
\(348\) 0 0
\(349\) −67.2666 116.509i −0.0103172 0.0178699i 0.860821 0.508908i \(-0.169951\pi\)
−0.871138 + 0.491038i \(0.836617\pi\)
\(350\) −5834.29 −0.891018
\(351\) 0 0
\(352\) −65.8332 −0.00996853
\(353\) −1486.85 2575.31i −0.224185 0.388300i 0.731890 0.681423i \(-0.238639\pi\)
−0.956075 + 0.293124i \(0.905305\pi\)
\(354\) 0 0
\(355\) 2123.50 3678.02i 0.317476 0.549884i
\(356\) 3396.56 0.505666
\(357\) 0 0
\(358\) 5198.36 9003.82i 0.767435 1.32924i
\(359\) −8671.60 −1.27485 −0.637423 0.770514i \(-0.719999\pi\)
−0.637423 + 0.770514i \(0.719999\pi\)
\(360\) 0 0
\(361\) 1.42682 + 2.47133i 0.000208022 + 0.000360304i
\(362\) −1976.77 3423.86i −0.287007 0.497111i
\(363\) 0 0
\(364\) −655.440 3283.60i −0.0943802 0.472823i
\(365\) −1074.68 −0.154113
\(366\) 0 0
\(367\) −2257.16 3909.52i −0.321043 0.556063i 0.659660 0.751564i \(-0.270700\pi\)
−0.980704 + 0.195501i \(0.937367\pi\)
\(368\) 1449.46 2510.55i 0.205322 0.355628i
\(369\) 0 0
\(370\) −849.530 + 1471.43i −0.119365 + 0.206746i
\(371\) 2158.28 3738.24i 0.302027 0.523126i
\(372\) 0 0
\(373\) −3285.30 + 5690.31i −0.456049 + 0.789901i −0.998748 0.0500270i \(-0.984069\pi\)
0.542699 + 0.839928i \(0.317403\pi\)
\(374\) −64.7190 112.097i −0.00894797 0.0154983i
\(375\) 0 0
\(376\) −8304.42 −1.13901
\(377\) 2076.61 + 10403.3i 0.283689 + 1.42121i
\(378\) 0 0
\(379\) 2745.19 + 4754.81i 0.372060 + 0.644427i 0.989882 0.141891i \(-0.0453181\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(380\) −643.982 1115.41i −0.0869357 0.150577i
\(381\) 0 0
\(382\) −685.188 −0.0917730
\(383\) 5093.63 8822.42i 0.679562 1.17704i −0.295551 0.955327i \(-0.595503\pi\)
0.975113 0.221709i \(-0.0711635\pi\)
\(384\) 0 0
\(385\) 118.328 0.0156638
\(386\) 1227.53 2126.14i 0.161864 0.280356i
\(387\) 0 0
\(388\) 2304.47 + 3991.47i 0.301526 + 0.522258i
\(389\) −4883.97 −0.636573 −0.318287 0.947995i \(-0.603107\pi\)
−0.318287 + 0.947995i \(0.603107\pi\)
\(390\) 0 0
\(391\) −6561.94 −0.848725
\(392\) −6484.52 11231.5i −0.835504 1.44714i
\(393\) 0 0
\(394\) −1675.32 + 2901.74i −0.214217 + 0.371035i
\(395\) 651.192 0.0829494
\(396\) 0 0
\(397\) 1057.52 1831.68i 0.133691 0.231560i −0.791406 0.611291i \(-0.790650\pi\)
0.925097 + 0.379732i \(0.123984\pi\)
\(398\) 5640.80 0.710422
\(399\) 0 0
\(400\) −1623.08 2811.26i −0.202885 0.351407i
\(401\) −337.127 583.921i −0.0419834 0.0727173i 0.844270 0.535918i \(-0.180034\pi\)
−0.886254 + 0.463201i \(0.846701\pi\)
\(402\) 0 0
\(403\) 7709.61 + 2611.29i 0.952960 + 0.322773i
\(404\) 4439.89 0.546765
\(405\) 0 0
\(406\) 7882.76 + 13653.3i 0.963583 + 1.66897i
\(407\) −34.9904 + 60.6051i −0.00426145 + 0.00738105i
\(408\) 0 0
\(409\) −2336.67 + 4047.23i −0.282496 + 0.489297i −0.971999 0.234986i \(-0.924496\pi\)
0.689503 + 0.724283i \(0.257829\pi\)
\(410\) −2024.93 + 3507.29i −0.243913 + 0.422470i
\(411\) 0 0
\(412\) 1752.35 3035.17i 0.209544 0.362942i
\(413\) 7803.67 + 13516.4i 0.929767 + 1.61040i
\(414\) 0 0
\(415\) −3255.90 −0.385122
\(416\) 3711.48 3259.29i 0.437429 0.384134i
\(417\) 0 0
\(418\) 61.0841 + 105.801i 0.00714766 + 0.0123801i
\(419\) −128.427 222.441i −0.0149739 0.0259355i 0.858441 0.512912i \(-0.171433\pi\)
−0.873415 + 0.486976i \(0.838100\pi\)
\(420\) 0 0
\(421\) −8746.82 −1.01257 −0.506287 0.862365i \(-0.668982\pi\)
−0.506287 + 0.862365i \(0.668982\pi\)
\(422\) 5126.74 8879.77i 0.591388 1.02431i
\(423\) 0 0
\(424\) 3602.43 0.412617
\(425\) −3673.96 + 6363.48i −0.419325 + 0.726293i
\(426\) 0 0
\(427\) 2997.63 + 5192.05i 0.339732 + 0.588433i
\(428\) −894.439 −0.101015
\(429\) 0 0
\(430\) 5815.95 0.652255
\(431\) 4381.36 + 7588.74i 0.489658 + 0.848113i 0.999929 0.0119008i \(-0.00378823\pi\)
−0.510271 + 0.860014i \(0.670455\pi\)
\(432\) 0 0
\(433\) −3212.75 + 5564.64i −0.356570 + 0.617597i −0.987385 0.158336i \(-0.949387\pi\)
0.630815 + 0.775933i \(0.282721\pi\)
\(434\) 12096.7 1.33793
\(435\) 0 0
\(436\) −987.836 + 1710.98i −0.108506 + 0.187939i
\(437\) 6193.39 0.677963
\(438\) 0 0
\(439\) −3410.14 5906.54i −0.370745 0.642149i 0.618935 0.785442i \(-0.287564\pi\)
−0.989680 + 0.143293i \(0.954231\pi\)
\(440\) 49.3763 + 85.5222i 0.00534982 + 0.00926616i
\(441\) 0 0
\(442\) 9198.39 + 3115.55i 0.989870 + 0.335275i
\(443\) −5062.48 −0.542948 −0.271474 0.962446i \(-0.587511\pi\)
−0.271474 + 0.962446i \(0.587511\pi\)
\(444\) 0 0
\(445\) −4502.94 7799.32i −0.479685 0.830839i
\(446\) 5450.20 9440.03i 0.578643 1.00224i
\(447\) 0 0
\(448\) 8242.65 14276.7i 0.869261 1.50560i
\(449\) −3295.41 + 5707.82i −0.346370 + 0.599930i −0.985602 0.169084i \(-0.945919\pi\)
0.639232 + 0.769014i \(0.279252\pi\)
\(450\) 0 0
\(451\) −83.4029 + 144.458i −0.00870796 + 0.0150826i
\(452\) −2168.44 3755.85i −0.225653 0.390842i
\(453\) 0 0
\(454\) −5109.52 −0.528198
\(455\) −6671.01 + 5858.24i −0.687344 + 0.603601i
\(456\) 0 0
\(457\) 1127.37 + 1952.67i 0.115397 + 0.199873i 0.917938 0.396723i \(-0.129853\pi\)
−0.802542 + 0.596596i \(0.796519\pi\)
\(458\) 2195.82 + 3803.28i 0.224026 + 0.388025i
\(459\) 0 0
\(460\) 1163.46 0.117928
\(461\) 3679.40 6372.90i 0.371728 0.643852i −0.618104 0.786097i \(-0.712099\pi\)
0.989831 + 0.142245i \(0.0454321\pi\)
\(462\) 0 0
\(463\) 11598.3 1.16419 0.582096 0.813120i \(-0.302233\pi\)
0.582096 + 0.813120i \(0.302233\pi\)
\(464\) −4385.91 + 7596.62i −0.438816 + 0.760052i
\(465\) 0 0
\(466\) −3385.44 5863.75i −0.336539 0.582903i
\(467\) 302.150 0.0299397 0.0149698 0.999888i \(-0.495235\pi\)
0.0149698 + 0.999888i \(0.495235\pi\)
\(468\) 0 0
\(469\) −3583.41 −0.352807
\(470\) 2558.59 + 4431.61i 0.251104 + 0.434925i
\(471\) 0 0
\(472\) −6512.66 + 11280.3i −0.635105 + 1.10003i
\(473\) 239.547 0.0232862
\(474\) 0 0
\(475\) 3467.61 6006.08i 0.334958 0.580164i
\(476\) −6267.05 −0.603466
\(477\) 0 0
\(478\) −2236.06 3872.97i −0.213965 0.370598i
\(479\) −1573.07 2724.64i −0.150053 0.259900i 0.781193 0.624289i \(-0.214611\pi\)
−0.931247 + 0.364389i \(0.881278\pi\)
\(480\) 0 0
\(481\) −1027.80 5149.06i −0.0974300 0.488101i
\(482\) 4283.24 0.404764
\(483\) 0 0
\(484\) −1611.42 2791.06i −0.151335 0.262121i
\(485\) 6110.25 10583.3i 0.572067 0.990849i
\(486\) 0 0
\(487\) −1534.08 + 2657.10i −0.142743 + 0.247238i −0.928529 0.371261i \(-0.878926\pi\)
0.785786 + 0.618499i \(0.212259\pi\)
\(488\) −2501.71 + 4333.09i −0.232064 + 0.401947i
\(489\) 0 0
\(490\) −3995.76 + 6920.85i −0.368388 + 0.638066i
\(491\) −50.2791 87.0859i −0.00462131 0.00800435i 0.863706 0.503997i \(-0.168138\pi\)
−0.868327 + 0.495992i \(0.834804\pi\)
\(492\) 0 0
\(493\) 19855.7 1.81390
\(494\) −8681.77 2940.57i −0.790711 0.267818i
\(495\) 0 0
\(496\) 3365.27 + 5828.82i 0.304647 + 0.527665i
\(497\) 9752.34 + 16891.6i 0.880186 + 1.52453i
\(498\) 0 0
\(499\) 3616.55 0.324447 0.162223 0.986754i \(-0.448133\pi\)
0.162223 + 0.986754i \(0.448133\pi\)
\(500\) 1623.58 2812.13i 0.145218 0.251524i
\(501\) 0 0
\(502\) 9830.40 0.874009
\(503\) −2686.32 + 4652.84i −0.238125 + 0.412445i −0.960176 0.279395i \(-0.909866\pi\)
0.722051 + 0.691840i \(0.243200\pi\)
\(504\) 0 0
\(505\) −5886.13 10195.1i −0.518672 0.898366i
\(506\) −110.359 −0.00969574
\(507\) 0 0
\(508\) 109.696 0.00958065
\(509\) −5657.37 9798.85i −0.492649 0.853293i 0.507315 0.861761i \(-0.330638\pi\)
−0.999964 + 0.00846746i \(0.997305\pi\)
\(510\) 0 0
\(511\) 2467.77 4274.30i 0.213636 0.370028i
\(512\) 11716.1 1.01130
\(513\) 0 0
\(514\) −7067.93 + 12242.0i −0.606524 + 1.05053i
\(515\) −9292.65 −0.795113
\(516\) 0 0
\(517\) 105.383 + 182.529i 0.00896469 + 0.0155273i
\(518\) −3901.52 6757.64i −0.330933 0.573192i
\(519\) 0 0
\(520\) −7017.75 2376.95i −0.591824 0.200454i
\(521\) 18470.9 1.55321 0.776606 0.629986i \(-0.216939\pi\)
0.776606 + 0.629986i \(0.216939\pi\)
\(522\) 0 0
\(523\) −5445.51 9431.90i −0.455288 0.788582i 0.543417 0.839463i \(-0.317130\pi\)
−0.998705 + 0.0508814i \(0.983797\pi\)
\(524\) −1273.79 + 2206.28i −0.106195 + 0.183935i
\(525\) 0 0
\(526\) −678.556 + 1175.29i −0.0562480 + 0.0974243i
\(527\) 7617.53 13193.9i 0.629649 1.09058i
\(528\) 0 0
\(529\) 3286.15 5691.78i 0.270087 0.467805i
\(530\) −1109.91 1922.42i −0.0909648 0.157556i
\(531\) 0 0
\(532\) 5915.06 0.482050
\(533\) −2449.87 12273.3i −0.199091 0.997400i
\(534\) 0 0
\(535\) 1185.79 + 2053.85i 0.0958247 + 0.165973i
\(536\) −1495.29 2589.92i −0.120497 0.208708i
\(537\) 0 0
\(538\) 14993.9 1.20155
\(539\) −164.577 + 285.056i −0.0131518 + 0.0227796i
\(540\) 0 0
\(541\) −13416.3 −1.06620 −0.533099 0.846053i \(-0.678973\pi\)
−0.533099 + 0.846053i \(0.678973\pi\)
\(542\) −3871.38 + 6705.42i −0.306808 + 0.531407i
\(543\) 0 0
\(544\) −4622.50 8006.40i −0.364316 0.631014i
\(545\) 5238.45 0.411726
\(546\) 0 0
\(547\) −17849.0 −1.39519 −0.697593 0.716495i \(-0.745745\pi\)
−0.697593 + 0.716495i \(0.745745\pi\)
\(548\) 1868.56 + 3236.45i 0.145659 + 0.252289i
\(549\) 0 0
\(550\) −61.7887 + 107.021i −0.00479033 + 0.00829709i
\(551\) −18740.5 −1.44895
\(552\) 0 0
\(553\) −1495.32 + 2589.97i −0.114987 + 0.199163i
\(554\) −9334.09 −0.715826
\(555\) 0 0
\(556\) 45.8553 + 79.4237i 0.00349766 + 0.00605812i
\(557\) −10065.7 17434.3i −0.765703 1.32624i −0.939874 0.341521i \(-0.889058\pi\)
0.174172 0.984715i \(-0.444275\pi\)
\(558\) 0 0
\(559\) −13505.0 + 11859.6i −1.02182 + 0.897328i
\(560\) −7341.02 −0.553955
\(561\) 0 0
\(562\) 485.801 + 841.433i 0.0364632 + 0.0631561i
\(563\) −11172.9 + 19352.0i −0.836380 + 1.44865i 0.0565220 + 0.998401i \(0.481999\pi\)
−0.892902 + 0.450251i \(0.851334\pi\)
\(564\) 0 0
\(565\) −5749.57 + 9958.55i −0.428117 + 0.741521i
\(566\) −6935.05 + 12011.9i −0.515021 + 0.892043i
\(567\) 0 0
\(568\) −8138.94 + 14097.1i −0.601237 + 1.04137i
\(569\) −4227.86 7322.87i −0.311496 0.539527i 0.667191 0.744887i \(-0.267497\pi\)
−0.978686 + 0.205360i \(0.934163\pi\)
\(570\) 0 0
\(571\) 12813.0 0.939069 0.469534 0.882914i \(-0.344422\pi\)
0.469534 + 0.882914i \(0.344422\pi\)
\(572\) −67.1741 22.7523i −0.00491030 0.00166315i
\(573\) 0 0
\(574\) −9299.65 16107.5i −0.676237 1.17128i
\(575\) 3132.41 + 5425.50i 0.227184 + 0.393494i
\(576\) 0 0
\(577\) 1971.59 0.142251 0.0711253 0.997467i \(-0.477341\pi\)
0.0711253 + 0.997467i \(0.477341\pi\)
\(578\) 3286.86 5693.01i 0.236532 0.409685i
\(579\) 0 0
\(580\) −3520.50 −0.252036
\(581\) 7476.47 12949.6i 0.533866 0.924683i
\(582\) 0 0
\(583\) −45.7149 79.1805i −0.00324754 0.00562491i
\(584\) 4119.02 0.291860
\(585\) 0 0
\(586\) −1183.14 −0.0834046
\(587\) 4292.85 + 7435.43i 0.301848 + 0.522816i 0.976555 0.215270i \(-0.0690632\pi\)
−0.674707 + 0.738086i \(0.735730\pi\)
\(588\) 0 0
\(589\) −7189.70 + 12452.9i −0.502965 + 0.871161i
\(590\) 8026.19 0.560056
\(591\) 0 0
\(592\) 2170.78 3759.90i 0.150707 0.261032i
\(593\) 1746.73 0.120961 0.0604803 0.998169i \(-0.480737\pi\)
0.0604803 + 0.998169i \(0.480737\pi\)
\(594\) 0 0
\(595\) 8308.46 + 14390.7i 0.572460 + 0.991530i
\(596\) 2206.99 + 3822.63i 0.151681 + 0.262720i
\(597\) 0 0
\(598\) 6221.70 5463.68i 0.425459 0.373623i
\(599\) −27531.1 −1.87794 −0.938972 0.343994i \(-0.888220\pi\)
−0.938972 + 0.343994i \(0.888220\pi\)
\(600\) 0 0
\(601\) 8769.54 + 15189.3i 0.595203 + 1.03092i 0.993518 + 0.113673i \(0.0362616\pi\)
−0.398315 + 0.917249i \(0.630405\pi\)
\(602\) −13355.1 + 23131.7i −0.904173 + 1.56607i
\(603\) 0 0
\(604\) −3923.00 + 6794.83i −0.264279 + 0.457744i
\(605\) −4272.64 + 7400.43i −0.287120 + 0.497306i
\(606\) 0 0
\(607\) 11345.5 19651.1i 0.758651 1.31402i −0.184887 0.982760i \(-0.559192\pi\)
0.943539 0.331263i \(-0.107475\pi\)
\(608\) 4362.88 + 7556.72i 0.291016 + 0.504055i
\(609\) 0 0
\(610\) 3083.11 0.204642
\(611\) −14977.9 5073.10i −0.991719 0.335901i
\(612\) 0 0
\(613\) −3607.65 6248.63i −0.237702 0.411713i 0.722352 0.691525i \(-0.243061\pi\)
−0.960055 + 0.279813i \(0.909728\pi\)
\(614\) −7056.44 12222.1i −0.463802 0.803329i
\(615\) 0 0
\(616\) −453.528 −0.0296642
\(617\) −8435.22 + 14610.2i −0.550387 + 0.953299i 0.447859 + 0.894104i \(0.352187\pi\)
−0.998246 + 0.0591947i \(0.981147\pi\)
\(618\) 0 0
\(619\) 2244.53 0.145743 0.0728717 0.997341i \(-0.476784\pi\)
0.0728717 + 0.997341i \(0.476784\pi\)
\(620\) −1350.62 + 2339.35i −0.0874876 + 0.151533i
\(621\) 0 0
\(622\) −52.5403 91.0025i −0.00338694 0.00586635i
\(623\) 41360.1 2.65981
\(624\) 0 0
\(625\) 1859.84 0.119030
\(626\) 11759.0 + 20367.1i 0.750771 + 1.30037i
\(627\) 0 0
\(628\) 1005.85 1742.18i 0.0639134 0.110701i
\(629\) −9827.44 −0.622966
\(630\) 0 0
\(631\) 1834.61 3177.63i 0.115744 0.200475i −0.802333 0.596877i \(-0.796408\pi\)
0.918077 + 0.396402i \(0.129741\pi\)
\(632\) −2495.88 −0.157090
\(633\) 0 0
\(634\) −9154.54 15856.1i −0.573459 0.993260i
\(635\) −145.428 251.889i −0.00908840 0.0157416i
\(636\) 0 0
\(637\) −4834.27 24218.6i −0.300692 1.50640i
\(638\) 333.933 0.0207218
\(639\) 0 0
\(640\) −1531.78 2653.12i −0.0946077 0.163865i
\(641\) 7339.30 12712.0i 0.452239 0.783300i −0.546286 0.837599i \(-0.683959\pi\)
0.998525 + 0.0542983i \(0.0172922\pi\)
\(642\) 0 0
\(643\) −2759.86 + 4780.22i −0.169266 + 0.293178i −0.938162 0.346196i \(-0.887473\pi\)
0.768896 + 0.639374i \(0.220807\pi\)
\(644\) −2671.64 + 4627.41i −0.163474 + 0.283145i
\(645\) 0 0
\(646\) −8578.08 + 14857.7i −0.522446 + 0.904902i
\(647\) −5663.43 9809.35i −0.344131 0.596052i 0.641065 0.767487i \(-0.278493\pi\)
−0.985195 + 0.171435i \(0.945160\pi\)
\(648\) 0 0
\(649\) 330.582 0.0199946
\(650\) −1814.97 9092.59i −0.109522 0.548678i
\(651\) 0 0
\(652\) −2518.84 4362.76i −0.151297 0.262054i
\(653\) 1951.44 + 3380.00i 0.116946 + 0.202557i 0.918556 0.395291i \(-0.129356\pi\)
−0.801610 + 0.597848i \(0.796023\pi\)
\(654\) 0 0
\(655\) 6754.87 0.402954
\(656\) 5174.26 8962.09i 0.307959 0.533400i
\(657\) 0 0
\(658\) −23501.0 −1.39235
\(659\) 4011.23 6947.66i 0.237110 0.410687i −0.722774 0.691085i \(-0.757133\pi\)
0.959884 + 0.280398i \(0.0904665\pi\)
\(660\) 0 0
\(661\) 2584.38 + 4476.27i 0.152074 + 0.263399i 0.931990 0.362485i \(-0.118072\pi\)
−0.779916 + 0.625884i \(0.784738\pi\)
\(662\) 3162.05 0.185645
\(663\) 0 0
\(664\) 12479.2 0.729346
\(665\) −7841.82 13582.4i −0.457282 0.792036i
\(666\) 0 0
\(667\) 8464.45 14660.9i 0.491372 0.851081i
\(668\) 208.248 0.0120619
\(669\) 0 0
\(670\) −921.396 + 1595.91i −0.0531293 + 0.0920227i
\(671\) 126.987 0.00730593
\(672\) 0 0
\(673\) 3327.05 + 5762.62i 0.190562 + 0.330063i 0.945437 0.325806i \(-0.105636\pi\)
−0.754875 + 0.655869i \(0.772302\pi\)
\(674\) 4474.30 + 7749.71i 0.255702 + 0.442890i
\(675\) 0 0
\(676\) 4913.51 2042.97i 0.279558 0.116236i
\(677\) 20649.4 1.17226 0.586130 0.810217i \(-0.300651\pi\)
0.586130 + 0.810217i \(0.300651\pi\)
\(678\) 0 0
\(679\) 28061.8 + 48604.4i 1.58603 + 2.74708i
\(680\) −6933.93 + 12009.9i −0.391036 + 0.677294i
\(681\) 0 0
\(682\) 128.112 221.896i 0.00719304 0.0124587i
\(683\) 14237.8 24660.6i 0.797649 1.38157i −0.123495 0.992345i \(-0.539410\pi\)
0.921144 0.389223i \(-0.127256\pi\)
\(684\) 0 0
\(685\) 4954.45 8581.36i 0.276350 0.478652i
\(686\) −6404.54 11093.0i −0.356453 0.617394i
\(687\) 0 0
\(688\) −14861.3 −0.823522
\(689\) 6497.37 + 2200.70i 0.359260 + 0.121683i
\(690\) 0 0
\(691\) −5305.41 9189.24i −0.292080 0.505897i 0.682221 0.731146i \(-0.261014\pi\)
−0.974301 + 0.225248i \(0.927681\pi\)
\(692\) −3277.64 5677.03i −0.180053 0.311862i
\(693\) 0 0
\(694\) 18410.3 1.00698
\(695\) 121.584 210.590i 0.00663590 0.0114937i
\(696\) 0 0
\(697\) −23424.6 −1.27299
\(698\) 158.868 275.167i 0.00861495 0.0149215i
\(699\) 0 0
\(700\) 2991.65 + 5181.68i 0.161534 + 0.279785i
\(701\) 13518.9 0.728390 0.364195 0.931323i \(-0.381344\pi\)
0.364195 + 0.931323i \(0.381344\pi\)
\(702\) 0 0
\(703\) 9275.49 0.497627
\(704\) −174.589 302.398i −0.00934671 0.0161890i
\(705\) 0 0
\(706\) 3511.60 6082.26i 0.187196 0.324234i
\(707\) 54064.9 2.87599
\(708\) 0 0
\(709\) −7422.69 + 12856.5i −0.393180 + 0.681008i −0.992867 0.119226i \(-0.961959\pi\)
0.599687 + 0.800235i \(0.295292\pi\)
\(710\) 10030.4 0.530190
\(711\) 0 0
\(712\) 17258.8 + 29893.2i 0.908430 + 1.57345i
\(713\) −6494.70 11249.1i −0.341134 0.590861i
\(714\) 0 0
\(715\) 36.8104 + 184.412i 0.00192536 + 0.00964561i
\(716\) −10662.2 −0.556517
\(717\) 0 0
\(718\) −10240.1 17736.4i −0.532254 0.921891i
\(719\) −17950.1 + 31090.4i −0.931049 + 1.61262i −0.149518 + 0.988759i \(0.547772\pi\)
−0.781531 + 0.623866i \(0.785561\pi\)
\(720\) 0 0
\(721\) 21338.6 36959.5i 1.10221 1.90908i
\(722\) −3.36981 + 5.83669i −0.000173700 + 0.000300857i
\(723\) 0 0
\(724\) −2027.25 + 3511.30i −0.104064 + 0.180244i
\(725\) −9478.32 16416.9i −0.485539 0.840978i
\(726\) 0 0
\(727\) 12951.4 0.660715 0.330357 0.943856i \(-0.392831\pi\)
0.330357 + 0.943856i \(0.392831\pi\)
\(728\) 25568.6 22453.4i 1.30170 1.14310i
\(729\) 0 0
\(730\) −1269.07 2198.09i −0.0643429 0.111445i
\(731\) 16819.9 + 29132.8i 0.851032 + 1.47403i
\(732\) 0 0
\(733\) −1105.36 −0.0556989 −0.0278494 0.999612i \(-0.508866\pi\)
−0.0278494 + 0.999612i \(0.508866\pi\)
\(734\) 5330.88 9233.35i 0.268074 0.464318i
\(735\) 0 0
\(736\) −7882.27 −0.394761
\(737\) −37.9504 + 65.7321i −0.00189677 + 0.00328531i
\(738\) 0 0
\(739\) −6819.03 11810.9i −0.339434 0.587917i 0.644892 0.764274i \(-0.276902\pi\)
−0.984326 + 0.176356i \(0.943569\pi\)
\(740\) 1742.45 0.0865591
\(741\) 0 0
\(742\) 10194.7 0.504391
\(743\) 5077.44 + 8794.38i 0.250704 + 0.434232i 0.963720 0.266916i \(-0.0860045\pi\)
−0.713016 + 0.701148i \(0.752671\pi\)
\(744\) 0 0
\(745\) 5851.79 10135.6i 0.287776 0.498442i
\(746\) −15518.2 −0.761611
\(747\) 0 0
\(748\) −66.3718 + 114.959i −0.00324438 + 0.00561943i
\(749\) −10891.7 −0.531338
\(750\) 0 0
\(751\) −13289.7 23018.5i −0.645738 1.11845i −0.984131 0.177446i \(-0.943217\pi\)
0.338393 0.941005i \(-0.390117\pi\)
\(752\) −6537.90 11324.0i −0.317038 0.549126i
\(753\) 0 0
\(754\) −18826.1 + 16532.4i −0.909294 + 0.798510i
\(755\) 20803.5 1.00280
\(756\) 0 0
\(757\) 6838.86 + 11845.3i 0.328352 + 0.568723i 0.982185 0.187916i \(-0.0601734\pi\)
−0.653833 + 0.756639i \(0.726840\pi\)
\(758\) −6483.48 + 11229.7i −0.310674 + 0.538103i
\(759\) 0 0
\(760\) 6544.49 11335.4i 0.312360 0.541024i
\(761\) 8998.36 15585.6i 0.428634 0.742415i −0.568118 0.822947i \(-0.692328\pi\)
0.996752 + 0.0805314i \(0.0256617\pi\)
\(762\) 0 0
\(763\) −12029.0 + 20834.8i −0.570744 + 0.988558i
\(764\) 351.343 + 608.544i 0.0166376 + 0.0288172i
\(765\) 0 0
\(766\) 24059.9 1.13488
\(767\) −18637.3 + 16366.6i −0.877383 + 0.770487i
\(768\) 0 0
\(769\) −1497.52 2593.78i −0.0702236 0.121631i 0.828776 0.559581i \(-0.189038\pi\)
−0.898999 + 0.437950i \(0.855705\pi\)
\(770\) 139.732 + 242.023i 0.00653972 + 0.0113271i
\(771\) 0 0
\(772\) −2517.75 −0.117378
\(773\) −13027.7 + 22564.7i −0.606177 + 1.04993i 0.385688 + 0.922629i \(0.373964\pi\)
−0.991864 + 0.127299i \(0.959369\pi\)
\(774\) 0 0
\(775\) −14545.3 −0.674169
\(776\) −23419.3 + 40563.5i −1.08338 + 1.87647i
\(777\) 0 0
\(778\) −5767.39 9989.41i −0.265772 0.460331i
\(779\) 22109.0 1.01686
\(780\) 0 0
\(781\) 413.133 0.0189284
\(782\) −7748.87 13421.4i −0.354346 0.613746i
\(783\) 0 0
\(784\) 10210.3 17684.7i 0.465117 0.805607i
\(785\) −5333.95 −0.242518
\(786\) 0 0
\(787\) 11496.0 19911.7i 0.520697 0.901874i −0.479013 0.877808i \(-0.659005\pi\)
0.999710 0.0240662i \(-0.00766123\pi\)
\(788\) 3436.21 0.155343
\(789\) 0 0
\(790\) 768.980 + 1331.91i 0.0346318 + 0.0599840i
\(791\) −26405.3 45735.4i −1.18693 2.05583i
\(792\) 0 0
\(793\) −7159.15 + 6286.91i −0.320591 + 0.281532i
\(794\) 4995.22 0.223267
\(795\) 0 0
\(796\) −2892.43 5009.84i −0.128793 0.223077i
\(797\) −12913.1 + 22366.2i −0.573910 + 0.994042i 0.422249 + 0.906480i \(0.361241\pi\)
−0.996159 + 0.0875619i \(0.972092\pi\)
\(798\) 0 0
\(799\) −14799.0 + 25632.6i −0.655258 + 1.13494i
\(800\) −4413.20 + 7643.89i −0.195038 + 0.337815i
\(801\) 0 0
\(802\) 796.214 1379.08i 0.0350565 0.0607196i
\(803\) −52.2704 90.5349i −0.00229711 0.00397872i
\(804\) 0 0
\(805\) 14167.6 0.620299
\(806\) 3763.14 + 18852.4i 0.164455 + 0.823882i
\(807\) 0 0
\(808\) 22560.3 + 39075.6i 0.982263 + 1.70133i
\(809\) −14247.9 24678.1i −0.619195 1.07248i −0.989633 0.143620i \(-0.954126\pi\)
0.370438 0.928857i \(-0.379208\pi\)
\(810\) 0 0
\(811\) 6992.41 0.302758 0.151379 0.988476i \(-0.451629\pi\)
0.151379 + 0.988476i \(0.451629\pi\)
\(812\) 8084.07 14002.0i 0.349378 0.605141i
\(813\) 0 0
\(814\) −165.278 −0.00711670
\(815\) −6678.64 + 11567.8i −0.287046 + 0.497179i
\(816\) 0 0
\(817\) −15875.2 27496.6i −0.679807 1.17746i
\(818\) −11037.3 −0.471773
\(819\) 0 0
\(820\) 4153.29 0.176877
\(821\) 15756.3 + 27290.8i 0.669793 + 1.16012i 0.977962 + 0.208784i \(0.0669507\pi\)
−0.308168 + 0.951332i \(0.599716\pi\)
\(822\) 0 0
\(823\) −19579.8 + 33913.2i −0.829293 + 1.43638i 0.0693001 + 0.997596i \(0.477923\pi\)
−0.898593 + 0.438782i \(0.855410\pi\)
\(824\) 35616.8 1.50579
\(825\) 0 0
\(826\) −18430.4 + 31922.4i −0.776364 + 1.34470i
\(827\) 36557.6 1.53716 0.768581 0.639752i \(-0.220963\pi\)
0.768581 + 0.639752i \(0.220963\pi\)
\(828\) 0 0
\(829\) −7337.59 12709.1i −0.307413 0.532454i 0.670383 0.742015i \(-0.266130\pi\)
−0.977796 + 0.209561i \(0.932797\pi\)
\(830\) −3844.83 6659.44i −0.160790 0.278497i
\(831\) 0 0
\(832\) 24814.0 + 8404.66i 1.03398 + 0.350215i
\(833\) −46223.3 −1.92262
\(834\) 0 0
\(835\) −276.082 478.188i −0.0114422 0.0198184i
\(836\) 62.6441 108.503i 0.00259162 0.00448881i
\(837\) 0 0
\(838\) 303.313 525.354i 0.0125033 0.0216564i
\(839\) −4257.78 + 7374.69i −0.175202 + 0.303459i −0.940231 0.340536i \(-0.889391\pi\)
0.765029 + 0.643996i \(0.222725\pi\)
\(840\) 0 0
\(841\) −13417.9 + 23240.6i −0.550164 + 0.952912i
\(842\) −10329.0 17890.3i −0.422755 0.732232i
\(843\) 0 0
\(844\) −10515.3 −0.428854
\(845\) −11205.2 8574.17i −0.456177 0.349066i
\(846\) 0 0
\(847\) −19622.4 33987.0i −0.796025 1.37876i
\(848\) 2836.12 + 4912.31i 0.114850 + 0.198926i
\(849\) 0 0
\(850\) −17354.0 −0.700281
\(851\) −4189.43 + 7256.31i −0.168757 + 0.292295i
\(852\) 0 0
\(853\) 9645.93 0.387187 0.193593 0.981082i \(-0.437986\pi\)
0.193593 + 0.981082i \(0.437986\pi\)
\(854\) −7079.69 + 12262.4i −0.283679 + 0.491347i
\(855\) 0 0
\(856\) −4544.89 7871.97i −0.181473 0.314321i
\(857\) −36139.6 −1.44050 −0.720248 0.693717i \(-0.755972\pi\)
−0.720248 + 0.693717i \(0.755972\pi\)
\(858\) 0 0
\(859\) −7108.04 −0.282332 −0.141166 0.989986i \(-0.545085\pi\)
−0.141166 + 0.989986i \(0.545085\pi\)
\(860\) −2982.24 5165.39i −0.118248 0.204812i
\(861\) 0 0
\(862\) −10347.7 + 17922.8i −0.408869 + 0.708182i
\(863\) −16225.8 −0.640016 −0.320008 0.947415i \(-0.603686\pi\)
−0.320008 + 0.947415i \(0.603686\pi\)
\(864\) 0 0
\(865\) −8690.57 + 15052.5i −0.341605 + 0.591677i
\(866\) −15175.5 −0.595478
\(867\) 0 0
\(868\) −6202.83 10743.6i −0.242555 0.420118i
\(869\) 31.6727 + 54.8588i 0.00123639 + 0.00214149i
\(870\) 0 0
\(871\) −1114.75 5584.64i −0.0433661 0.217254i
\(872\) −20077.9 −0.779727
\(873\) 0 0
\(874\) 7313.66 + 12667.6i 0.283053 + 0.490262i
\(875\) 19770.5 34243.5i 0.763846 1.32302i
\(876\) 0 0
\(877\) 15491.5 26832.0i 0.596477 1.03313i −0.396860 0.917879i \(-0.629900\pi\)
0.993337 0.115249i \(-0.0367667\pi\)
\(878\) 8053.94 13949.8i 0.309576 0.536201i
\(879\) 0 0
\(880\) −77.7458 + 134.660i −0.00297819 + 0.00515838i
\(881\) −3835.38 6643.07i −0.146671 0.254042i 0.783324 0.621614i \(-0.213523\pi\)
−0.929995 + 0.367572i \(0.880189\pi\)
\(882\) 0 0
\(883\) −34340.6 −1.30878 −0.654390 0.756157i \(-0.727075\pi\)
−0.654390 + 0.756157i \(0.727075\pi\)
\(884\) −1949.60 9767.03i −0.0741766 0.371607i
\(885\) 0 0
\(886\) −5978.19 10354.5i −0.226683 0.392627i
\(887\) −9604.17 16634.9i −0.363559 0.629702i 0.624985 0.780637i \(-0.285105\pi\)
−0.988544 + 0.150935i \(0.951772\pi\)
\(888\) 0 0
\(889\) 1335.78 0.0503943
\(890\) 10634.9 18420.1i 0.400541 0.693758i
\(891\) 0 0
\(892\) −11178.8 −0.419611
\(893\) 13967.8 24193.0i 0.523422 0.906593i
\(894\) 0 0
\(895\) 14135.3 + 24483.1i 0.527924 + 0.914390i
\(896\) 14069.6 0.524591
\(897\) 0 0
\(898\) −15566.0 −0.578444
\(899\) 19652.2 + 34038.6i 0.729074 + 1.26279i
\(900\) 0 0
\(901\) 6419.77 11119.4i 0.237373 0.411143i
\(902\) −393.956 −0.0145425
\(903\) 0 0
\(904\) 22036.9 38169.0i 0.810770 1.40430i
\(905\) 10750.4 0.394868
\(906\) 0 0
\(907\) 23240.5 + 40253.7i 0.850813 + 1.47365i 0.880475 + 0.474092i \(0.157224\pi\)
−0.0296621 + 0.999560i \(0.509443\pi\)
\(908\) 2620.00 + 4537.98i 0.0957576 + 0.165857i
\(909\) 0 0
\(910\) −19859.8 6726.63i −0.723457 0.245039i
\(911\) 34109.3 1.24050 0.620248 0.784406i \(-0.287032\pi\)
0.620248 + 0.784406i \(0.287032\pi\)
\(912\) 0 0
\(913\) −158.361 274.289i −0.00574039 0.00994264i
\(914\) −2662.59 + 4611.74i −0.0963573 + 0.166896i
\(915\) 0 0
\(916\) 2251.90 3900.41i 0.0812280 0.140691i
\(917\) −15511.1 + 26866.0i −0.558584 + 0.967497i
\(918\) 0 0
\(919\) 18766.8 32505.1i 0.673623 1.16675i −0.303246 0.952912i \(-0.598070\pi\)
0.976869 0.213837i \(-0.0685962\pi\)
\(920\) 5911.86 + 10239.6i 0.211857 + 0.366947i
\(921\) 0 0
\(922\) 17379.7 0.620793
\(923\) −23291.2 + 20453.5i −0.830596 + 0.729399i
\(924\) 0 0
\(925\) 4691.24 + 8125.46i 0.166753 + 0.288825i
\(926\) 13696.3 + 23722.6i 0.486055 + 0.841872i
\(927\) 0 0
\(928\) 23850.8 0.843687
\(929\) 2483.37 4301.33i 0.0877038 0.151907i −0.818836 0.574027i \(-0.805380\pi\)
0.906540 + 0.422120i \(0.138714\pi\)
\(930\) 0 0
\(931\) 43627.2 1.53579
\(932\) −3471.89 + 6013.50i −0.122023 + 0.211351i
\(933\) 0 0
\(934\) 356.803 + 618.001i 0.0124999 + 0.0216505i
\(935\) 351.966 0.0123107
\(936\) 0 0
\(937\) −5096.90 −0.177704 −0.0888519 0.996045i \(-0.528320\pi\)
−0.0888519 + 0.996045i \(0.528320\pi\)
\(938\) −4231.58 7329.31i −0.147298 0.255128i
\(939\) 0 0
\(940\) 2623.93 4544.78i 0.0910459 0.157696i
\(941\) −54774.8 −1.89756 −0.948781 0.315933i \(-0.897682\pi\)
−0.948781 + 0.315933i \(0.897682\pi\)
\(942\) 0 0
\(943\) −9985.91 + 17296.1i −0.344842 + 0.597284i
\(944\) −20509.1 −0.707113
\(945\) 0 0
\(946\) 282.877 + 489.957i 0.00972210 + 0.0168392i
\(947\) −6884.24 11923.9i −0.236228 0.409159i 0.723401 0.690428i \(-0.242578\pi\)
−0.959629 + 0.281269i \(0.909245\pi\)
\(948\) 0 0
\(949\) 7429.08 + 2516.28i 0.254118 + 0.0860714i
\(950\) 16379.4 0.559386
\(951\) 0 0
\(952\) −31844.6 55156.4i −1.08413 1.87776i
\(953\) 17933.3 31061.4i 0.609566 1.05580i −0.381746 0.924267i \(-0.624677\pi\)
0.991312 0.131532i \(-0.0419897\pi\)
\(954\) 0 0
\(955\) 931.578 1613.54i 0.0315656 0.0546732i
\(956\) −2293.17 + 3971.88i −0.0775798 + 0.134372i
\(957\) 0 0
\(958\) 3715.23 6434.96i 0.125296 0.217019i
\(959\) 22753.7 + 39410.5i 0.766167 + 1.32704i
\(960\) 0 0
\(961\) 366.899 0.0123158
\(962\) 9317.89 8182.64i 0.312288 0.274240i
\(963\) 0 0
\(964\) −2196.31 3804.12i −0.0733801 0.127098i
\(965\) 3337.87 + 5781.37i 0.111347 + 0.192859i
\(966\) 0 0
\(967\) −24476.5 −0.813972 −0.406986 0.913434i \(-0.633420\pi\)
−0.406986 + 0.913434i \(0.633420\pi\)
\(968\) 16376.1 28364.3i 0.543749 0.941800i
\(969\) 0 0
\(970\) 28861.9 0.955362
\(971\) −4488.03 + 7773.50i −0.148329 + 0.256914i −0.930610 0.366012i \(-0.880723\pi\)
0.782281 + 0.622926i \(0.214056\pi\)
\(972\) 0 0
\(973\) 558.383 + 967.149i 0.0183977 + 0.0318657i
\(974\) −7246.26 −0.238383
\(975\) 0 0
\(976\) −7878.18 −0.258376
\(977\) −21001.4 36375.5i −0.687711 1.19115i −0.972576 0.232583i \(-0.925282\pi\)
0.284865 0.958568i \(-0.408051\pi\)
\(978\) 0 0
\(979\) 438.029 758.688i 0.0142998 0.0247679i
\(980\) 8195.60 0.267142
\(981\) 0 0
\(982\) 118.747 205.676i 0.00385884 0.00668370i
\(983\) −43240.7 −1.40301 −0.701507 0.712662i \(-0.747489\pi\)
−0.701507 + 0.712662i \(0.747489\pi\)
\(984\) 0 0
\(985\) −4555.51 7890.38i −0.147361 0.255237i
\(986\) 23447.2 + 40611.7i 0.757312 + 1.31170i
\(987\) 0 0
\(988\) 1840.10 + 9218.47i 0.0592524 + 0.296841i
\(989\) 28681.2 0.922152
\(990\) 0 0
\(991\) −18958.3 32836.7i −0.607698 1.05256i −0.991619 0.129198i \(-0.958760\pi\)
0.383921 0.923366i \(-0.374574\pi\)
\(992\) 9150.26 15848.7i 0.292864 0.507255i
\(993\) 0 0
\(994\) −23032.7 + 39893.8i −0.734963 + 1.27299i
\(995\) −7669.20 + 13283.5i −0.244352 + 0.423230i
\(996\) 0 0
\(997\) −3317.43 + 5745.96i −0.105380 + 0.182524i −0.913893 0.405954i \(-0.866939\pi\)
0.808513 + 0.588478i \(0.200273\pi\)
\(998\) 4270.71 + 7397.09i 0.135458 + 0.234620i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 117.4.g.e.55.3 8
3.2 odd 2 39.4.e.c.16.2 8
12.11 even 2 624.4.q.i.289.3 8
13.3 even 3 1521.4.a.v.1.2 4
13.9 even 3 inner 117.4.g.e.100.3 8
13.10 even 6 1521.4.a.bb.1.3 4
39.2 even 12 507.4.b.h.337.3 8
39.11 even 12 507.4.b.h.337.6 8
39.23 odd 6 507.4.a.i.1.2 4
39.29 odd 6 507.4.a.m.1.3 4
39.35 odd 6 39.4.e.c.22.2 yes 8
156.35 even 6 624.4.q.i.529.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.e.c.16.2 8 3.2 odd 2
39.4.e.c.22.2 yes 8 39.35 odd 6
117.4.g.e.55.3 8 1.1 even 1 trivial
117.4.g.e.100.3 8 13.9 even 3 inner
507.4.a.i.1.2 4 39.23 odd 6
507.4.a.m.1.3 4 39.29 odd 6
507.4.b.h.337.3 8 39.2 even 12
507.4.b.h.337.6 8 39.11 even 12
624.4.q.i.289.3 8 12.11 even 2
624.4.q.i.529.3 8 156.35 even 6
1521.4.a.v.1.2 4 13.3 even 3
1521.4.a.bb.1.3 4 13.10 even 6